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NATURALLY ORDERED TRANSFORMATION SEMIGROUPS PRESERVING AN EQUIVALENCE

Part of: Semigroups

Published online by Cambridge University Press:  01 August 2008

LEI SUN ,
HUISHENG PEI  and
ZHENGXING CHENG
LEI SUN*
Affiliation:
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan, 454003, PR China (email: [email protected])
HUISHENG PEI
Affiliation:
Department of Mathematics, Xinyang Normal University, Xinyang, Henan, 464000, PR China (email: [email protected])
ZHENGXING CHENG
Affiliation:
School of Sciences, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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Let 𝒯X be the full transformation semigroup on a set X and E be a nontrivial equivalence on X. Write then TE(X) is a subsemigroup of 𝒯X. In this paper, we endow TE(X) with the so-called natural order and determine when two elements of TE(X) are related under this order, then find out elements of TE(X) which are compatible with ≤ on TE(X). Also, the maximal and minimal elements and the covering elements are described.

Keywords

natural ordercompatibilitythe maximal(minimal) elementsthe covering elements

MSC classification

Secondary: 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 1 , August 2008 , pp. 117 - 128
Copyright
Copyright © 2008 Australian Mathematical Society

References

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